## THERMAL SCIENCE

International Scientific Journal

### A FRACTIONAL MODEL FOR HEAT TRANSFER IN MONGOLIAN YURT

**ABSTRACT**

A yurt is a portable tent-like dwelling structure favored by Mongolian nomads for more than three millennia and it can be favorably used even at a harsh environment as low as -50 degrees. The paper concludes that the multi-layer structure of the felt cover is the key for weatherproofing. A fractional differential model with He's fractional derivative is established to find an optimal thickness of the fractal hierarchy of the felt cover. A better understanding of the yurt mechanism could help the further design of yurt-like space suits and other protective clothing for extreme cold region.

**KEYWORDS**

PAPER SUBMITTED: 2015-01-10

PAPER REVISED: 2016-05-05

PAPER ACCEPTED: 2016-07-12

PUBLISHED ONLINE: 2017-09-09

**THERMAL SCIENCE** YEAR

**2017**, VOLUME

**21**, ISSUE

**4**, PAGES [1861 - 1866]

- Humphrey, C., Inside a Mongolian Tent, New Society, 30 (1974), 630, pp. 273-275
- Manfield, P., A Comparative Study of Temporary Shelters Used in Cold Climates, M. Ph. thesis, Cambridge University, Cambridge, UK, 2000
- Nielsen, R., et al., Thermal Function of a Clothing Ensemble during Work: Dependency on Inner Clothing Layer Fit, Ergonomics, 32 (1989), 12, pp. 1581-1594
- Guo, X. F., et al., Study on Thermal Properties of Tibetan Robe Ensemble in Different Wearing Ways, Advanced Materials Research, 332-334 (2011), Sept., pp. 367-370
- Li, J., et al., Temperature Rating Prediction of Tibetan Robe Ensemble Based on Different Wearing Ways, Applied Ergonomics, 43 (2012), 5, pp. 909-915
- Liu, H. Y., He, J.-H., From Leibniz's Notation for Derivative to the Fractal Derivative, Fractional Derivative and Application in Mongolian Yurt, in: Fractional Dynamics (Ed. C. Cattani, H. M. Srivastava, X.-J., Yang), De Gruyter, Berlin, 2016, pp. 219-228
- Chen, R., et al., Silk Cocoon: "Emperor's New Clothes" for Pupa: Fractal Nano-Hydrodynamical Approach, Journal of Nano Research, 22 (2013), May, pp. 65-70
- Yang, X. J., Advanced Local Fractional Calculus and Its Applications, World Science, New York, USA, 2012
- Jumarie, G., Fractional Partial Differential Equations and Modified Riemann-Liouville Derivative New Methods for Solution, Journal of Applied Mathematics and Computing, 24 (2007), 1-2, pp. 31-48
- He, J.-H., A Tutorial Review on Fractal Spacetime and Fractional Calculus, International Journal of Theoretical Physics, 53 (2014), 11, pp. 3698-3718
- Liu, F. J., et al., He's Fractional Derivative for Heat Conduction in a Fractal Medium Arising in Silkworm Cocoon Hierarchy, Thermal Science, 19 (2015), 4, pp. 1155-1159
- Liu, F. J., et al., A Fractional Model for Insulation Clothings with Cocoon-Like Porous Structure, Thermal Science, 20 (2016), 3, pp. 779-784
- Fan, J., He, J.-H., Biomimic Design of Multi-Scale Fabric with Efficient Heat Transfer Property, Thermal Science, 16 (2012), 5, pp. 1349-1352
- Fan, J., He, J.-H., Fractal Derivative Model for Air Permeability in Hierarchic Porous Media, Abstract and Applied Analysis, 2012 (2012), ID 354701
- Wang, K. L., Liu, S. Y., A New Solution Procedure for Nonlinear Fractional Porous Media Equation Based on a New Fractional Derivative, Nonlinear Science Letters A, 7 (2016), 4, pp. 135-140
- Wang, K. L., Liu, S. Y., He's Fractional Derivative for Nonlinear Fractional Heat Transfer Equation, Thermal Science, 20 (2016), 3, pp. 793-796
- Sayevand, K., Pichaghchi, K., Analysis of Nonlinear Fractional KdV Equation Based on He's Fractional Derivative, Nonlinear Science Letters A, 7 (2016), 3, pp. 77-85
- Li, Z. B., He, J.-H., Fractional Complex Transform for Fractional Differential Equations, Mathematical & Computational Applications, 15 (2010), 5, pp. 970-973
- He, J.-H., Li, Z. B., Converting Fractional Differential Equations into Partial Differential Equations, Thermal Science,16 (2012), 2, pp. 331-334
- He, J.-H., et al., Geometrical Explanation of the Fractional Complex Transform and Derivative Chain Rule for Fractional Calculus, Physics Letters A, 376 (2012), 4, pp. 257-259